GRAS versus minimizing absolute and squared differences: a comment

Junius and Oosterhaven (2003) Junius, T. and Oosterhaven, J. 2003. The solution of updating or regionalizing a matrix with both positive and negative entries. Economic Systems Research, 15: 87–96. [Taylor & Francis Online] , [Google Scholar] developed the GRAS algorithm that minimizes the information gain when updating input–output tables with both positive and negative signs. Jackson and Murray (2004) Jackson, R. W. and Murray, A. T. 2004. Alternative input–output matrix updating formulations. Economic Systems Research, 16: 135–148. [Taylor & Francis Online] , [Google Scholar], however, claim that minimizing squared differences in coefficients produces a smaller information gain, which is theoretically impossible. In this comment, calculation errors are sorted out from differences in measures, and it is shown that the information gain needs to be taken in absolute terms when increasing and decreasing cell values occur together. The numerical results show that GRAS outperforms both sign-preserving alternatives in all but one comparison of lesser economic importance. Moreover, as opposed to the result of Jackson and Murray, they show that minimizing absolute differences consistently outperforms minimizing squared differences, which overweighs large errors in small coefficients.